The number of troops will increase to about 6,000 in the lead-up to the Pan American Games which will be held in Rio in July.
The national force will initially stay out of the city, but will patrol highways and guard state borders to crack down on drug and gun smuggling.
Jose Luiz Goncalves, a lieutenant and leader of a Sao Paulo-based platoon, told Agencia Estado: "We still don't know exactly what our mission is, but whatever it is, we'll give a good account."
Violent crime, fueled largely by poverty, is a huge problem in Brazil.
But crime-fighting has been hampered by disputes over whether it is a federal or a state responsibility.
The national security force was set up two years ago to bolster state police forces.
Drugs gangs control many of Rio's slums, and police often enter only in military-style invasions.
Last week, a report by Washington-based Human Rights Watch said police violence, torture and extrajudicial killings were still widespread in the fight against violent crime Brazil, despite government efforts to rein them in.
Meanwhile, Alexandre Siqueira de Andrade, a lieutenant colonel and the commander of a Rio police battalion, was killed on Saturday in a shoot-out with two men who were stealing his car.